Given the true identity of the murderer, it actually makes a bit of sense that a few possible deaths involve Laura being killed by the murderer. As mentioned, the mysterious figure doesn't even look at her - so it's not that hard to think Lillian simply either mistook her for someone else (one of the intended targets), was in the closet with a victim and thus Laura had seen and she had to kill her to keep her quiet, or maybe as Lillian gets more and more unhinged, she lashes out at Laura. This still doesn't explain the shower death beyond simple Easter Egg / Shout-Out.
It's also misdirection on the developers' part - one of the deaths is also in the secret passages. Obviously, the killer is also using the secret passages as well... so this not only can back up Rudy's claim that it was the Colonel, in the Bad Ending, but it also can foreshadow that it is indeed Lillian - as Lillian basically grew up in the house, it's not unlikely to think she may have discovered the secret passages.
In the first game, there's several ways for Laura to get murdered by an unseen figure, even very early in the game. But once you've beaten the game, it's obvious that nobody had any motive to kill her, especially not the murderer, and certainly not that early in the night. She was actually the only person present who the murderer didn't want to kill.
If you take a look at the instances in which Laura can be killed by the mysterious figure, taking a shower, hiding in the attic, the closet and hidden passages, Laura is simply grabbed and killed without the murderer even looking.
The shower thing makes no sense, as the killer would recognize Laura's blue dress even if they couldn't make out Laura herself, but the others do. We know that the killer's moving the bodies from the murder scene to the laundry chute. Maybe Laura saw Lillian hiding in the closet with the latest victim. Laura's very last realization would be that her best friend is a murderer and even she's not safe from her.
If you really think about it, even though she's not part of the family Lillian invited Laura to kill her.
